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Improvement on observer-based $H_{\infty}$ control for T--S fuzzy systems. (English) Zbl 1093.93016
Summary: This paper provides an improved result over that in {\it X. Liu} and {\it Q. Zhang} [New approaches to $H_\infty$ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica 39, 1571--1582 (2003; Zbl 1029.93042)] for the problem of observer-based $H_{\infty}$ control for nonlinear systems in Takagi-Sugeno (T-S) fuzzy model. It contributes in three aspects: (i) The present result is less conservative than that in {\it X. Liu} and {\it Q. Zhang} [loc. cit.]; (ii) The present strict LMI method is a single step approach which overcomes the drawback of a two-step approach in {\it X. Liu} and {\it Q. Zhang} [loc. cit.]; (iii) The matrix dimensions are largely reduced compared with the corresponding ones in Liu and Zhang [loc. cit.].

##### MSC:
 93C42 Fuzzy control systems 93B36 $H^\infty$-control 93B07 Observability
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##### References:
 [1] Kim, E.; Lee, H.: New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE transactions on fuzzy systems 8, No. 5, 523-534 (2000) [2] Liu, X.; Zhang, Q.: New approaches to H$\infty$controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica 39, 1571-1582 (2003) · Zbl 1029.93042 [3] Nguang, S. K.; Shi, P.: H$\infty$fuzzy output feedback control design for nonlinear systems: an LMI approach. IEEE transactions on fuzzy systems 11, No. 3, 331-340 (2003) [4] Takagi, T.; Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE transactions on systems, man and cybernatics 15, 116-132 (1985) · Zbl 0576.93021 [5] Wang, L. X.: Adaptive fuzzy systems and control: design and stability analysis. (1994)